Prerequisites

A booted Raspberry Pi with keyboard, mouse, monitor

A network connection (Ethernet or WiFi).

Authorization to use root privileges.

Installing the software

Login to the computer, activate a web browser, and navigate to the [|Oracle Java SE Downloads] download page.
[The Midori browser has had trouble interfacing to this page. This page has been successfully handled using the Iceweasel browser.]
Click on the JDK Download link.
Read and accept the Oracle Binary Code License Agreement for Java SE.
Download the current file for "Linux ARM v6/v7 Soft Float ABI" and save in a location where you have write access. Your home directory will be assumed for the following instructions.

The following directions assume that you are installing version 7u10 of the JDK. Adjust the filenames appropriately if you downloaded and are installing a different version.

Activate a terminal window by either double click on either of the "LXTerminal" or "Root Terminal" icons or menu "Accessories -> LXTerminal" or "Accessories -> Root Terminal". Type the following commands in the terminal to create an installation directory and unpack the downloaded file:

This should create directory /opt/java/jdk1.7.0_10 (or similar, depending on the version you downloaded).
If the tar command completes correctly, the downloaded file in your home directory can be deleted:

rm ~/jdk-7u10-linux-arm-sfp.tar.gz

The system needs to know that a JVM has been installed, where it can be found on the system, and which is the default version (if there is more than one choice available). Type the following in the command window:

To use all java programs, you need to define a JAVA_HOME environment variable and add the associated bin directory to the system PATH. Edit the file /etc/environment with an editor of your choice (eg. nano):

sudo nano "/etc/environment"

and add:

JAVA_HOME="/opt/java/jdk1.7.0_10"

Similarly, add the following line in an appropriate place in your ~/.bashrc file: